Simplify to lowest terms. $\dfrac{78}{130}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 78 and 130? $78 = 2\cdot3\cdot13$ $130 = 2\cdot5\cdot13$ $\mbox{GCD}(78, 130) = 2\cdot13 = 26$ $\dfrac{78}{130} = \dfrac{3 \cdot 26}{ 5\cdot 26}$ $\hphantom{\dfrac{78}{130}} = \dfrac{3}{5} \cdot \dfrac{26}{26}$ $\hphantom{\dfrac{78}{130}} = \dfrac{3}{5} \cdot 1$ $\hphantom{\dfrac{78}{130}} = \dfrac{3}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{78}{130}= \dfrac{2\cdot39}{2\cdot65}= \dfrac{2\cdot 13\cdot3}{2\cdot 13\cdot5}= \dfrac{3}{5}$